Near Ocho Rios, there is a nice two hour mountain bike ride up to the summit of Murphy Hill at 1,800 feet above sea level. The route is on dirt roads and grass paths.
Note: If you plan to bring your own bike to the island, make sure it is very clean in order to avoid problems with Agriculture Officers at the airport. Otherwise, they may want to pull your bike out and spray it with some chemical. Also, there really are not any maintained trails. All the vegetation grows very fast and the trails become brushy. And, the rain makes the trails very slippery so it is better to try during the dry season from January through April. It is guarenteed to be hot and humid.
Overall, Murphy Hill is the 3rd most popular mountain bike trail of all 3 mountain biking rides in Jamaica.